Analysis of Stochastic Volatility Sequences Generated by Product Autoregressive Models

The classical methods of analysing time series by Box-Jenkins approach assume that the observed series uctuates around changing levels with constant variance. That is, the time series is assumed to be of homoscedastic nature. However, the nancial time series exhibits the presence of heteroscedasticity in the sense that, it possesses non-constant conditional variance given the past observations. So, the analysis of nancial time series, requires the modelling of such variances, which may depend on some time dependent factors or its own past values. This lead to introduction of several classes of models to study the behaviour of nancial time series. See Taylor (1986), Tsay (2005), Rachev et al. (2007). The class of models, used to describe the evolution of conditional variances is referred to as stochastic volatility modelsThe stochastic models available to analyse the conditional variances, are based on either normal or log-normal distributions. One of the objectives of the present study is to explore the possibility of employing some non-Gaussian distributions to model the volatility sequences and then study the behaviour of the resulting return series. This lead us to work on the related problem of statistical inference, which is the main contribution of the thesis

Novel Hetrocyclic Constructions Mediated by Nucleophilic Carbenes and Related Chemistry

The thesis entitled novel heterocyclic constructions mediated by nucleophilic carbenes and related chemistry, embodies the results of the investigations carried out to explore the reactivity patterns of the 1:1 zwitterions, generated in situ from various nucleophilic carbenes and DiMethyl AcetyleneDicarboxylate(DMAD) towards aldehydes and ketones. The traditional synthesis of complex organic molecules employs stepwise formation of bonds and involves multiple steps. Besides the sequential synthesis, in several instances, the desired product can also be obtained in one pot reactions of three or more starting compounds. Such reactions in which more than two starting materials react to form a product in such a way that the majority of the atoms of the starting materials can be found in the products are called multicomponent reactions(MCRs). The results of our investigations on the application of N-heterocyclic carbenes in multicomponent reaction with DMAD and aromatic aldehydes leading to the one pot synthesis of 2-oxy-maleate and furanone derivatives. It is interesting to note that dihydrofuran and lactone motifs are present in a number of biologically active natural products and other heterocyclic compounds. It is conceivable that the novel multicomponent reactions described herein will find application in the synthesis of a variety of heterocyclic compounds, and in natural product synthesis.

Studies on the Rheology and the Mechanical Properties of Thermoplastic Elastomer from Latex Product Waste and High Density Polyethylene

Latex waste products contain rubber hydrocarbon of very high quality, which is only lightly cross linked. Selected wastes such as thread waste and glove waste were modified into processable materials by a novel economic process and thermoplastic elastomers were prepared by blending these modified waste materials with high density polyethylene in various proportions. The mechanical properties as well as the rheological behaviour of these blends were evaluated and compared with those of the natural rubber-high density polyethylene blends.

Oxidation kinetics of nickel nano crystallites obtained by controlled thermolysis of diaquabis(ethylenediamine) nickel(II) nitrate

The metal complex, [Ni(en)2(H2O)2](NO3)2 (en = ethylenediamine), was decomposed in a static furnace at 200 C by autogenous decomposition to obtain phase pure metallic nickel nanocrystallites. The nickel metal thus obtained was studied by XRD, IR spectra, SEM and CHN analysis. The nickel crystallites are in the nanometer range as indicated by XRD studies. The IR spectral studies and CHN analyses show that the surface is covered with a nitrogen containing species. Thermogravimetric mass gain shows that the product purity is high (93%). The formed nickel is stable and resistant to oxidation up to 350 C probably due to the coverage of nitrogen containing species. Activation energy for the oxidation of the prepared nickel nanocrystallites was determined by non-isothermal methods and was found to depend on the conversion ratio. The oxidation kinetics of the nickel crystallites obeyed a Johnson–Mehl–Avrami mechanism probably due to the special morphology and crystallite strain present on the metal.

Catalysis By Ferrites And Cobaltites For The Alkylation And Oxidation Of Organic Compounds

Catalysis is a very important process from an industrial point of view since the production of most industrially important chemicals involves catalysis.Solid acid catalysts are appealing since the nature of acid sites is known and their chemical behavior in acid catalyzed reactions can be rationalized by means of existing theories and models. Mixed oxides crystallizing in spinel structure are of special interest because the spinel lattice imparts extra stability to the catalyst under various reaction conditions so that theses systems have sustained activities for longer periods. The thesis entitled" Catalysis By Ferrites And Cobaltites For The Alkylation And Oxidation Of Organic Compounds " presents the preparation ,characterization ,and activity studies of the prepared spinels were modified by incorporating other ions and by changing the stoichiometry.The prepared spinels exhibiting better catalytic activity towards the studied reactions with good product selectivity.Acid-base properties and cation distribution of the spinels were found to control the catalytic activity.

Studies on Catalysis by Titania

Scientists throughout the world are in search of a better methodology to reduce the use of environmentally hazardous chemicals common in industries .A significant contribution in this field is given by different redox catalysts in oxidation reactions. The oxidation of organic substrates represents one of the most important industrial chemical reactions, explaining the significant efforts invested in the research and development of new heterogeneous catalysts with increased activities and selectivities in these type reactions[l-4|. Hence liquid phase reactions like epoxidation of cylcohexene and hydroxylation of phenol were carried out with a new outlook in the challenge using CeO2/TiO;; and CuO/TiO2 catalysts denoted as TiO2-Ce as TiO2-Cu respectively in this work. Also different wt% of metals incorporated titania catalysts like 3, 6, 9 wt% CeO2/TiO; and CuO/TiO;were subjected to the present study .The interaction between metal oxides and the oxide supports have attracted much attention because of the wide applications of supported metal oxide systems[7,8]. It is well known that supported oxides of transition metals are widely used as catalysts for various reactions. Titania as well its metal modified catalysts systems afford high activity and selectivity in the liquid phase epoxidation of cyclohexene[9]. Cyclohexene epoxide is obtained as the major product during the reaction with small amounts of allylic substitution products.This chapter gives an idea about the liquid phase oxidation reactions like epoxidation of cylcohexene and hydroxylation of phenol in which many industrially important products are formed. Here discusses about the redox properties of the ceria and copper incorporated titania catalysts.The epoxidation of cyclohcxene is carried out efficiently over the prepared systems with the selective formation of cyclohexane epoxide. This reaction hints that it might be possible to create cleaner nylon chemistry. The total acidity of the prepared systems plays an important role in determining the catalytic activity in the dehydrogenation of cyclohexane and cyclohexene. The total acidity of the prepared systems plays an important role in determining the catalytic activity in the dehydrogenation of cyclohexane and cyclohexene.

A study on fuzzy semi inner product spaces

Mathematical models are often used to describe physical realities. However, the physical realities are imprecise while the mathematical concepts are required to be precise and perfect. Even mathematicians like H. Poincare worried about this. He observed that mathematical models are over idealizations, for instance, he said that only in Mathematics, equality is a transitive relation. A first attempt to save this situation was perhaps given by K. Menger in 1951 by introducing the concept of statistical metric space in which the distance between points is a probability distribution on the set of nonnegative real numbers rather than a mere nonnegative real number. Other attempts were made by M.J. Frank, U. Hbhle, B. Schweizer, A. Sklar and others. An aspect in common to all these approaches is that they model impreciseness in a probabilistic manner. They are not able to deal with situations in which impreciseness is not apparently of a probabilistic nature. This thesis is confined to introducing and developing a theory of fuzzy semi inner product spaces.